I am responsible for a site that cannot be restarted during the day. I occasionally get a panic emergency report, and have to try to do some debugging without restarting. This is challenging at best, and sometimes impossible, because verbose logging is off and performance mode is on, meaning no SQL in the log and file watching doesn't work. So I'm limited in what I can do, and the various Notices sometimes are enough to at least give me a clue as to where to look.
I guess what I'm saying is that I'd miss them, and I think that most people in my situation would feel the same way, but there may not be enough of us to justify inflicting the log clutter on everyone.
Maybe the answer is to create a new logging level for production servers? Having debug on isn't the answer, since that gives way more detail than you need on a regular basis.